.svg){kind=logo}
ON THE CENTRALIZER OF AN AD-INVERTIBLE ELEMENT IN THE FIRST WEYL ALGEBRA OVER A NONZERO CHARACTERISTIC FIELD
Keywords:
Weyl algebras, centralizers, ad-invertible elementsDOI:
https://doi.org/10.17654/0972555525039Abstract
In this paper, we extend the result of Guccione et al. [1] about the centralizer of an ad-invertible element to a field of nonzero characteristic. Indeed, we have proved that, in a nonzero characteristic field, for any element $d \in A_1$, if there exists $e \in A_1$ such that $[e, d]=1$, then the centralizer of $d$ is equal to the polynomial algebra $C[d]$, i.e., $Z(d)=C[d]$, where $C$ is the center of $A_1$.
Received: September 5, 2025
Accepted: October 3, 2025
References
[1] J. A. Guccione, J. J. Guccione and C. Valqui, On the centralizer in the Weyl algebra, Article in Proceedings of the American Mathematical Society, 2009.
[2] N. Lauritzen and J. F. Thomsen, Two properties of endomorphisms of Weyl algebras, Journal of Algebra 479 (2017), 137-158.
[3] J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968), 209-242.
[4] Yoshifumi Tsuchimoto, Preliminaries on Dixmier Conjecture, Mem. Fac. Sci. Kochi Univ., Ser. A Math. 24 (2003), 43-59.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
